You've got to physically and mentally become that person you are portraying," Robert De Niro famously proclaimed when he was starring in Martin Scorsese's Taxi Driver (1976). Before shooting began, De Niro got himself a cab driver's licence and spent nights in New York picking up customers. His preparation for Scorsese's Raging Bull (1980) was even more gruelling: he went on a binge eating trip across Europe and put on more than 60lb in order to show ageing middleweight boxer Jake LaMotta in his declining years.

Such extreme dedication was only what we expected from the best American "Method" actors who learned their craft with Lee Strasberg at the Actors Studio or studied with other prominent, Stanislavski-influenced acting gurus such as Stella Adler (Marlon Brando's mentor) and Sanford Meisner. The actors' instinct was to immerse themselves utterly in their roles.

This isn't an approach that was much embraced this side of the Atlantic until recently. However, in films from Bronson to The Machinist, from Shame to Hunger, the likes of Tom Hardy, Christian Bale and Michael Fassbender have brought a brooding, introspective intensity to their performances that has occasionally made even their more illustrious American predecessors seem half-hearted by comparison.

Irish raised Fassbender won the Best Actor award at the Venice Film Festival this week for his performance as the sex-addicted New Yorker in Steve McQueen's Shame. What is startling is the reckless energy he brings to the role. "Shame examines a person who has all the Western freedoms and through his apparent sexual freedom creates his own prison," McQueen commented of the Fassbender character in his Director's Statement. "As we witness – and become desensitised to – the continued and continual sexualisation of society, how does anyone navigate through this maze and not be tainted by the surroundings? It is this 'elephant in the room' that I wish to explore."

The sex scenes, graphic and joyless, must have been very gruelling indeed to shoot. Fassbender talked in Venice about "just having to jump into it... the most important thing is to make sure everybody involved is comfortable, as much as they can be, and then just go for it, so you don't have to do many takes."

His real challenge wasn't the nudity required or even the physicality of the role, but in portraying a troubled and suffering character. This is something that a porn actor simply couldn't have done. (There's an emotional resonance to Shame that you don't find, for example, in the films that French auteur Catherine Breillat made with Italian porn star Rocco Siffredi.) Fassbender's Brandon doesn't have a huge amount of dialogue. Nonetheless, his anguish grows increasingly obvious. In certain scenes, when we see him roaming forlornly through the New York streets, being beaten up outside a bar or humiliating himself in a gay brothel, he invokes memories of Brando's grief-stricken Lothario in Last Tango in Paris (1972). At the same time, he shares the social awkwardness of De Niro's Travis Bickle in Taxi Driver, who tries to woo political campaigner Betsy (Cybill Shepherd) by taking her to an all-night porno theatre to watch a blue movie.

It's a mark of pride for Method actors that they have a chameleon-like ability to switch personality as they switch roles. In the early 1950s, Brando went from playing a paraplegic war veteran in The Men (1950) to portraying the swaggering, ultra-macho Stanley Kowalski in A Streetcar Named Desire (1951). In his recent film career, Fassbender has been undergoing some similarly radical transformations. He is a suitably saturnine and whiskered Mr Rochester in the new screen version of Jane Eyre. In David Cronenberg's A Dangerous Method, he plays Carl Jung in detached fashion, as someone always analysing and fascinated by his own instincts. There's a mix of pathos and even comedy in the scenes in which he is shown, still formally dressed, very solemnly spanking his patient Sabina (Keira Knightley), with whom he starts an affair. By complete contrast, in his breakthrough role as IRA prisoner Bobby Sands in Hunger (2008), he is portraying a character who (as director Steve McQueen puts it) is "using his body as a political tool."

De Niro used to talk about actors using their bodies as an instrument – "It's like knowing how to play the piano." The extreme transformations he underwent in the name of his craft are matched by those of Fassbender, Bale and Hardy in their best-known movies.

Bale famously denied himself food and sleep in preparation for The Machnist, turning himself into a jagged, pale-looking ghoul. In today's digital era, you'd expect the same cadaverous shape could be achieved through the use of doubles and computer simulation. What Bale realised, though, was that CGI and artificial performance-capture techniques like those used in Polar Express or Beowulf would never enable him really to inhabit a character: to match the gait, bearing, energy levels or mood swings of a long-term insomniac.

Hardy went to similar extremes when he played Britain's "most violent prisoner", Charles Bronson, in Nicolas Winding Refn's stylised 2008 biopic, shaving his head, putting on weight and muscling up. The role in Bronson came quick on the heels of an earlier film, Stuart: A Life Backwards (2007), for which he had been shedding the pounds to play a homeless drug addict.

Arguably, the rise of British Method acting started in earnest with some of the more extreme performances of Daniel Day-Lewis in the late 1980s and early 1990s.

Day-Lewis self-consciously rejected the British theatrical tradition of screen acting and looked to the Method instead. Cast members on Jim Sheridan's My Left Foot tell stories about how he stayed in character throughout the shooting of the film. As he was playing Christy Brown, an artist with cerebral palsy, this required extraordinary physical dedication.

"He'd call you by your film name, and you'd call him Christy. It was madness. You'd be feeding him, wheeling him around. During the entire film, I only saw him walking once," actress turned director Kirsten Sheridan (who appeared in the film) told me of working with Day-Lewis on the film.

Another important factor in changing British attitudes toward screen acting was the increasing prominence of directors such as Mike Leigh, Ken Loach and (in his TV work) Alan Clarke, whose work featured working-class characters. In their different ways, all three encouraged their actors to embrace a far more realist approach to their craft. As the renegade Mancunian adrift in east London, David Thewlis gave an astonishing performance in Leigh's Naked (1993), bringing an emotional intensity and bristling sarcasm to the role. Actors such as Ray Winstone, Gary Oldman and Tim Roth, who cut their teeth in Clarke movies including Scum, The Firm and Made in Britain, had a physicality that more buttoned-up British screen actors from an earlier generation had always lacked.

Traditionally, RADA-trained British actors, who had done their stints in seaside rep or in the West End, had been far more inclined to use technique rather than delve into the darkest corners of their psyches. There was (they perceived) something uncouth and unseemly about the Method. This was underlined by Laurence Olivier's alleged put-down of Dustin Hoffman during the shooting of Marathon Man (1976). Startled by the intense and self-lacerating physical routine that Hoffman put himself through in the run-up to the torture scene in the movie, Olivier is said to have asked his American co-star: "Have you tried acting, dear boy?"

It makes a droll enough anecdote, but also hints at why British screen acting often seemed so timorous by comparison with the work of the great Method stars. Brando, James Dean and co had realised that the movie camera registers the smallest look or tic or gesture. They knew that to be truly effective on screen, it wasn't enough just to sketch in a few personality traits. They had to inhabit their characters.

A counter-argument can be made that some of the greatest British screen performances came precisely because they were so restrained. Think of Michael Redgrave in The Browning Version (1951) or Trevor Howard in Brief Encounter (1945) and The Heart of the Matter (1953). Playing mediocre middle-class men, disappointed in their careers or sex lives, Howard and Redgrave are able to convey their characters' sense of yearning in the subtlest fashion. There are no "You was my brother, Charley, you shoulda looked out for me a little bit" style soliloquies like the ones Marlon Brando has in On the Waterfront. Instead, you see the loss and foreboding in their eyes. The very fact that they're bound by class and convention and that they're not extravagantly expressive in their gestures gives their performances an added resonance.

Like Olivier, Howard was disdainful of Method acting. He was appalled by Brando's off-screen antics and lack of punctuality on the set of Mutiny on the Bounty. "He may be the biggest bloody star in Christendom," Howard complained to one journalist, "but the man can't act." The ever-changing Alec Guinness has a fair claim as one of the greatest character actors in film history. Beneath his bland, Stan Laurel-like expression, he could always hint at a sense of seething inner turmoil.

Even so, the British suspicion of the Method didn't do its movie actors any favours. For too long, there was the sense that they looked down on cinema as little more than a lucrative sideline to their stage work. As Day-Lewis once said of Olivier, he "might have been a much better actor on film if he hadn't had that flippant attitude. [He] was a remarkable actor, but he was entirely missing the point consistently. He felt that film was an inferior form."

The difference with the newer generation of screen actors is that they don't suffer from their predecessors' snobberies or insecurities about movies. They're ready to throw themselves headlong into new roles. Whether they're playing sex addicts, gangsters, boxers, IRA hunger strikers, or even (in Bale's case) superheroes such as Batman, they approach new films with a ferocity and attention to detail that only De Niro and co. in their pomp could match. The fact that they're now so often playing Americans suggests that when it comes to Method, Britain may now even be the first port of call for casting agents.